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Title: Φ3 theory with F4 flavor symmetry in 6 – 2ϵ dimensions: 3-loop renormalization and conformal bootstrap

Abstract

Here, we consider Φ3 theory in 6 – 2ϵ with F4 global symmetry. The beta function is calculated up to 3 loops, and a stable unitary IR fixed point is observed. The anomalous dimensions of operators quadratic or cubic in Φ are also computed. We then employ conformal bootstrap technique to study the fixed point predicted from the perturbative approach. For each putative scaling dimension of Φ(ΔΦ), we obtain the corresponding upper bound on the scaling dimension of the second lowest scalar primary in the 26 representation (Δ262nd) which appears in the OPE of Φ × Φ. In D = 5.95, we observe a sharp peak on the upper bound curve located at ΔΦ equal to the value predicted by the 3-loop computation. In D = 5, we observe a weak kink on the upper bound curve at (ΔΦ, Δ262nd) = (1.6, 4).

Authors:
 [1];  [2];  [3]
  1. Max-Plack-Insitut fuer Gravitationsphysik, Potsdam (Germany)
  2. Inst. for Basic Sciences, Daejeon (Korea). Fields, Gravity & Strings, Center for Theoretical Physics
  3. Chinese Academy of Sciences (CAS), Beijing (China). CAS Key Lab. of Theoretical Physics
Publication Date:
Research Org.:
Texas A&M Univ., College Station, TX (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1465392
Grant/Contract Number:  
FG02-13ER42020; SC0010813
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 12; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal and W Symmetry; Global Symmetries

Citation Formats

Pang, Yi, Rong, Junchen, and Su, Ning. Φ3 theory with F4 flavor symmetry in 6 – 2ϵ dimensions: 3-loop renormalization and conformal bootstrap. United States: N. p., 2016. Web. doi:10.1007/JHEP12(2016)057.
Pang, Yi, Rong, Junchen, & Su, Ning. Φ3 theory with F4 flavor symmetry in 6 – 2ϵ dimensions: 3-loop renormalization and conformal bootstrap. United States. https://doi.org/10.1007/JHEP12(2016)057
Pang, Yi, Rong, Junchen, and Su, Ning. Wed . "Φ3 theory with F4 flavor symmetry in 6 – 2ϵ dimensions: 3-loop renormalization and conformal bootstrap". United States. https://doi.org/10.1007/JHEP12(2016)057. https://www.osti.gov/servlets/purl/1465392.
@article{osti_1465392,
title = {Φ3 theory with F4 flavor symmetry in 6 – 2ϵ dimensions: 3-loop renormalization and conformal bootstrap},
author = {Pang, Yi and Rong, Junchen and Su, Ning},
abstractNote = {Here, we consider Φ3 theory in 6 – 2ϵ with F4 global symmetry. The beta function is calculated up to 3 loops, and a stable unitary IR fixed point is observed. The anomalous dimensions of operators quadratic or cubic in Φ are also computed. We then employ conformal bootstrap technique to study the fixed point predicted from the perturbative approach. For each putative scaling dimension of Φ(ΔΦ), we obtain the corresponding upper bound on the scaling dimension of the second lowest scalar primary in the 26 representation (Δ262nd) which appears in the OPE of Φ × Φ. In D = 5.95, we observe a sharp peak on the upper bound curve located at ΔΦ equal to the value predicted by the 3-loop computation. In D = 5, we observe a weak kink on the upper bound curve at (ΔΦ, Δ262nd) = (1.6, 4).},
doi = {10.1007/JHEP12(2016)057},
journal = {Journal of High Energy Physics (Online)},
number = 12,
volume = 2016,
place = {United States},
year = {Wed Dec 14 00:00:00 EST 2016},
month = {Wed Dec 14 00:00:00 EST 2016}
}

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Works referenced in this record:

Bootstrapping 3D fermions
journal, March 2016

  • Iliesiu, Luca; Kos, Filip; Poland, David
  • Journal of High Energy Physics, Vol. 2016, Issue 3
  • DOI: 10.1007/JHEP03(2016)120

The N = 2 $$ \mathcal{N}=2 $$ superconformal bootstrap
journal, March 2016

  • Beem, Christopher; Lemos, Madalena; Liendo, Pedro
  • Journal of High Energy Physics, Vol. 2016, Issue 3
  • DOI: 10.1007/JHEP03(2016)183

Improved bounds for CFT’s with global symmetries
journal, January 2012


Bootstrapping the O(N ) vector models
journal, June 2014

  • Kos, Filip; Poland, David; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2014, Issue 6
  • DOI: 10.1007/JHEP06(2014)091

Precision islands in the Ising and O(N ) models
journal, August 2016

  • Kos, Filip; Poland, David; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2016, Issue 8
  • DOI: 10.1007/JHEP08(2016)036

Bootstrapping O(N ) vector models with four supercharges in 3 ≤ d ≤ 4
journal, May 2016

  • Chester, Shai M.; Iliesiu, Luca V.; Pufu, Silviu S.
  • Journal of High Energy Physics, Vol. 2016, Issue 5
  • DOI: 10.1007/JHEP05(2016)103

Models for strong interactions in 6−ϵ dimensions
journal, November 1976


Constraints on perturbative RG flows in six dimensions
journal, August 2016

  • Stergiou, Andreas; Stone, David; Vitale, Lorenzo G.
  • Journal of High Energy Physics, Vol. 2016, Issue 8
  • DOI: 10.1007/JHEP08(2016)010

Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model
journal, August 1952


Conformal Invariance and the Yang-Lee Edge Singularity in Two Dimensions
journal, April 1985


Quantum field theory in the large N limit: a review
journal, October 2003


Bounding scalar operator dimensions in 4 D CFT
journal, December 2008


N = 4 Superconformal Bootstrap
journal, August 2013


Challenge to the a Theorem in Six Dimensions
journal, December 2014


Φ3 theory in six dimensions and the renormalization group
journal, July 1974


Yang-Lee Edge Singularity and ϕ 3 Field Theory
journal, June 1978


An SU(3)×SU(3) field theory of strong interactions in 6-ϵ dimensions
journal, September 1977


Critical Exponents in 3.99 Dimensions
journal, January 1972


The N = 8 $$ \mathcal{N}=8 $$ superconformal bootstrap in three dimensions
journal, September 2014

  • Chester, Shai M.; Lee, Jaehoon; Pufu, Silviu S.
  • Journal of High Energy Physics, Vol. 2014, Issue 9
  • DOI: 10.1007/JHEP09(2014)143

Asymptotic Freedom and a "Quark" Model in Six Dimensions
journal, December 1975


A semidefinite program solver for the conformal bootstrap
journal, June 2015


The octonions
journal, December 2001


Tensor representations of conformal algebra and conformally covariant operator product expansion
journal, March 1973


Bootstrapping mixed correlators in the 3D Ising model
journal, November 2014

  • Kos, Filip; Poland, David; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2014, Issue 11
  • DOI: 10.1007/JHEP11(2014)109

Conformal four point functions and the operator product expansion
journal, April 2001


Conformal partial waves and the operator product expansion
journal, February 2004


Critical exponents to order ϵ 3 for ϕ 3 models of critical phenomena in 6-ϵ dimensions
journal, July 1980

  • Bonfim, O. F. de Alcantara; Kirkham, J. E.; McKane, A. J.
  • Journal of Physics A: Mathematical and General, Vol. 13, Issue 7
  • DOI: 10.1088/0305-4470/13/7/006

Statistical Theory of Equations of State and Phase Transitions. I. Theory of Condensation
journal, August 1952


Bootstrapping the Three Dimensional Supersymmetric Ising Model
journal, July 2015


Critical Sp(N ) models in 6 − ϵ dimensions and higher spin dS/CFT
journal, September 2015

  • Fei, Lin; Giombi, Simone; Klebanov, Igor R.
  • Journal of High Energy Physics, Vol. 2015, Issue 9
  • DOI: 10.1007/JHEP09(2015)076

Works referencing / citing this record:

Scalar CFTs and Their Large N Limits
text, January 2017


The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
text, January 2018